![自定义标题](https://linux22.com/image/469398/%E8%87%AA%E5%AE%9A%E4%B9%89%E6%A0%87%E9%A2%98.png)
我正在为考试制作一份试卷,我试图将我的徽标放在试卷上,但我失败了,所以我把它放在页眉上,它出现在每一页上。如何摆脱它,我希望它成为第一页。我看到了一些在线解决方案,但没有用,所以我问了这个问题。
代码:
\documentclass[A4, 10pt]{exam}
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\usepackage{draftwatermark}
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\SetWatermarkText{Math Vision}
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\thispagestyle{firstpage}
\lhead{Math Vision}
\chead{\includegraphics[scale=0.15]{logo13}}
\rhead{9038882708}
\lfoot{Math Vision}
\rfoot{903*****08}
\begin{document}
\begin{center}
\fbox{\fbox{\parbox{5.5in}{\centering
JEE MCQ TEST\\
Trigonometric set-1 }}}
\end{center}
\vspace{0.1in}
\makebox[\textwidth]{Name:\enspace\hrulefill}\\
\pointsinrightmargin
\textmd{Choose the correct answer:}
\begin{questions}
\question $\left(1+\cos \dfrac{\pi}{8}\right)\left(1+\cos \dfrac{3\pi}{8}\right)\left(1+\cos \dfrac{5\pi}{8}\right)\left(1+\cos \dfrac{7\pi}{8}\right)$ is equal to
\begin{oneparchoices}
\choice $\dfrac{1}{2}$
\choice $\cos \dfrac{\pi}{8}$
\choice $\dfrac{1}{8}$
\choice $\dfrac{1+\sqrt{2}}{2\sqrt{2}}$
\end{oneparchoices}
\question Which of the following number is rational?
\begin{oneparchoices}
\choice $\sin 15^{\circ}$
\choice $\cos 15^{\circ}$
\choice $\sin 12^{\circ}\cos 15^{\circ}$
\choice $\sin 15^{\circ}\cos 75^{\circ}$
\end{oneparchoices}
\question If $\alpha+\beta=\dfrac{\pi}{2}$ and $\beta+\gamma=\alpha$ the, $\tan \alpha$ is
\begin{oneparchoices}
\choice $2(\tan \beta+\tan \gamma)$
\choice $\tan \beta+\tan \gamma$
\choice $\tan \beta+2\tan \gamma$
\choice $2\tan\beta\tan\gamma$
\end{oneparchoices}
\question Given, both $\theta$ and $\phi$ are acute angles and $\sin \theta=\dfrac{1}{2}\cos \phi$ then the value of of $\theta+\phi$ is belongs to
\begin{oneparchoices}
\choice $\left(\dfrac{\pi}{3},\dfrac{\pi}{6}\right]$
\choice $\left(\dfrac{\pi}{2},\dfrac{2\pi}{3}\right)$
\choice $\left(\dfrac{2\pi}{3},\dfrac{5\pi}{6}\right]$
\choice $\left[\dfrac{5\pi}{6},\pi\right]$
\end{oneparchoices}
\question Given $\alpha+\beta+\gamma=\pi$, then the value of $\sin^2\alpha+\sin^2\beta-\sin^2\gamma$ is
\begin{oneparchoices}
\choice $2\sin\alpha\sin\beta\cos\gamma$
\choice $2\sin\alpha\cos\beta\sin\gamma$
\choice $\cos\alpha\sin\beta\sin\gamma$
\choice $\sin\gamma\sin\alpha\sin\beta$
\end{oneparchoices}
\question Find the value of $\sin 12^{\circ}\sin 48^{\circ}\sin 54^{\circ}$
\begin{oneparchoices}
\choice $\dfrac{1}{8}$
\choice $\dfrac{3}{8}$
\choice $\dfrac{-1}{8}$
\choice $\dfrac{-3}{8}$
\end{oneparchoices}
\question Prove that the value of the function $\dfrac{\sin x\sin 3x}{\sin 3x\cos x}$ do not lies between $\dfrac{1}{3}$ and 3 for any real $x$.
\question If $0^{\circ}<\theta<180^{\circ}$, then $\sqrt{2+\sqrt{2+\sqrt{2+\cdots+\sqrt{2(1+\cos\theta)}}}},$ then
\begin{oneparchoices}
\choice
\choice
\choice
\choice
\end{oneparchoices}
\question If $\tan \dfrac{\alpha}{2}$ and $\tan \dfrac{\beta}{2}$ are the two roots of the equation $8x^2-26x+15=0$ then $\cos (\alpha+\beta)$ is equal to
\begin{oneparchoices}
\choice $\dfrac{627}{725}$
\choice $\dfrac{627}{725}$
\choice $-1$
\choice None
\end{oneparchoices}
\question If $\sin \alpha=\sin \alpha,\cos \alpha= \cos \beta$ then
\begin{oneparchoices}
\choice $\sin \dfrac{\alpha+\beta}{2}$
\choice $\cos \dfrac{\alpha+\beta}{2}$
\choice $\sin \dfrac{\alpha-\beta}{2}$
\choice $\cos \dfrac{\alpha-\beta}{2}$
\end{oneparchoices}
\question If $\pi<\alpha<\dfrac{3\pi}{2},$ then the expression $\sqrt{4\sin^4\alpha+\sin^22\alpha}+4\cos^2 \left(\dfrac{\pi}{4}-\alpha/2\right)$ is equal to
\begin{oneparchoices}
\choice $2+4\sin \alpha$
\choice $2-4\sin\alpha$
\choice 2
\choice None
\end{oneparchoices}
\question If $A=\sin^8\theta+\cos^{14}\theta$, then for all values of $\theta$
\begin{oneparchoices}
\choice $A\geq 1$
\choice $0<A<1$
\choice $1<2A\leq 3$
\choice None
\end{oneparchoices}
\question If $2\cos\theta+\sin\theta=1,$ then $7\cos\theta+6\sin\theta$ equals
\begin{oneparchoices}
\choice 1 or 2
\choice 2 or 3
\choice 2 or 4
\choice 2 or 6
\end{oneparchoices}
\question The ratio of the greatest and least value of $2-\cos x+\sin^2x$ is
\begin{oneparchoices}
\choice $\dfrac{1}{4}$
\choice $\dfrac{9}{4}$
\choice $\dfrac{13}{4}$
\choice None
\end{oneparchoices}
\question For any real theta $\theta$, the maximum value of $\cos^2(\cos\theta)+\sin^2(\sin\theta)$
\begin{oneparchoices}
\choice 1
\choice 1+ $\sin^2 1$
\choice $1+\cos^2 1$
\choice None
\end{oneparchoices}
\question If $\cos^4\theta\sec^2\alpha,\dfrac{1}{2},\sin^4\theta\cosec^2\alpha$ are in A.P. then $\cos^8\theta\sec^6\alpha,\dfrac{1}{2},\sin^8\theta\cosec^6\alpha$ are in
\begin{oneparchoices}
\choice A.P.
\choice G.P.
\choice H.P.
\choice None
\end{oneparchoices}
\question The value of $4\sin A\cos^3A-4\cos A\sin ^3A$ is
\begin{oneparchoices}
\choice $\cos 2A$
\choice $\sin 3A$
\choice $\sin 2A$
\choice $\cos 4A$
\end{oneparchoices}
\question $\sin^6\theta+\cos^6\theta+3\sin^2\theta\cos^2\theta$ is equal to
\begin{oneparchoices}
\choice 0
\choice 1
\choice -1
\choice None
\end{oneparchoices}
\question The sum $S=\sin\theta+\sin2\theta+\sin3\theta+\cdots+\sin n\theta$ is
\begin{oneparchoices}
\choice $\dfrac{\sin \frac{(n+1)\theta}{2}\sin \frac{n\theta}{2}}{\sin \frac{\theta}{2}}$
\choice $\dfrac{\cos \frac{(n+1)\theta}{2}\sin \frac{n\theta}{2}}{\sin \frac{\theta}{2}}$
\choice $\dfrac{\sin \frac{(n+1)\theta}{2}\cos \frac{n\theta}{2}}{\sin \frac{\theta}{2}}$
\choice $\dfrac{\cos \frac{(n+1)\theta}{2}\cos \frac{n\theta}{2}}{\sin \frac{\theta}{2}}$
\end{oneparchoices}
\question If $a=\dfrac{\pi}{8}$, then $\cos a+\cos2a+\cos3a+\cdots+\cos18a$ is
\begin{oneparchoices}
\choice 0
\choice -1
\choice 1
\choice $\pm 1$
\choice None
\end{oneparchoices}
\question The expression $\dfrac{\cos6x+6\cos4x+15\cos2x+10}{\cos5x+5\cos3x+10\cos x}$ is
\begin{oneparchoices}
\choice $2\cos x$
\choice $\cos2x$
\choice $\cos^2x$
\choice None
\end{oneparchoices}
\question The value of $\sin \dfrac{\pi}{14}\cdot \sin \dfrac{3\pi}{14}\cdot \sin \dfrac{4\pi}{14}$ is
\begin{oneparchoices}
\choice $\dfrac{1}{16}$
\choice $\dfrac{1}{8}$
\choice $\dfrac{1}{2}$
\choice 1
\end{oneparchoices}
\question The numerical value of $\cos \dfrac{\pi}{7}+\cos \dfrac{3\pi}{7}+\cos \dfrac{5\pi}{7}$ is
\begin{oneparchoices}
\choice $\dfrac{-1}{2}$
\choice $\dfrac{3}{2}$
\choice $\dfrac{-3}{2}$
\choice $\dfrac{1}{2}$
\end{oneparchoices}
\question $\tan \dfrac{7\pi}{6},\tan \dfrac{9\pi}{4},\tan \dfrac{10\pi}{3}$ are in
\begin{oneparchoices}
\choice A.P.
\choice G.P.
\choice H.P.
\choice None
\end{oneparchoices}
\question If $\theta$ lies between 2nd and 3rd quadrant, then value of $\sqrt{\dfrac{1-\sin\theta}{1+\sin\theta}}+\sqrt{\dfrac{1+\sin\theta}{1-\sin\theta}}$ is
\begin{oneparchoices}
\choice $2\sec\theta$
\choice $-2\sec\theta$
\choice $2\cosec\theta$
\choice 1
\end{oneparchoices}
\question If $y=\dfrac{2\sin\alpha}{1+\cos\alpha-\sin\alpha}$ then $\dfrac{1-\cos\alpha+\sin\alpha}{1+\sin\alpha}$ is
\begin{oneparchoices}
\choice $\dfrac{1}{y}$
\choice $y$
\choice $1-y$
\choice $1+y$
\end{oneparchoices}
\question If $\cos(x-y),\cos x,\cos(x+y)$ are in H.P., then $\bigg|\cos x\sec \dfrac{y}{2}\bigg|$ is
\begin{oneparchoices}
\choice 2
\choice $\sqrt{2}$
\choice 1
\choice None
\end{oneparchoices}
\question If $\alpha,\beta,\gamma,\delta$ satisfy the equation $\tan (x+\dfrac{\pi}{4})=3\tan3x$ then $\tan\alpha+\tan\beta+\tan\gamma+\tan\delta\equiv \sum \tan\alpha$ is
\begin{oneparchoices}
\choice -1
\choice $\dfrac{1}{3}$
\choice 0
\choice 2
\end{oneparchoices}
\question If $\tan x=\dfrac{b}{a}$ then $\sqrt{\dfrac{a+b}{a-b}}+\sqrt{\dfrac{a-b}{a+b}}$ is
\begin{oneparchoices}
\choice $\dfrac{2\sin x}{\sqrt{2x}}$
\choice $\dfrac{2\cos x}{\sqrt{2x}}$
\choice $\dfrac{2\cos x}{\sqrt{\sin2x}}$
\choice $\dfrac{2\sin x}{\sqrt{\cos 2x}}$
\end{oneparchoices}
\question If $\cos x=\dfrac{2\cos y-1}{2-\cos y},x,y\in (0,\pi)$, then $\tan \dfrac{x}{2}\cot \dfrac{y}{2}$ is
\begin{oneparchoices}
\choice $\sqrt{2}$
\choice $\sqrt{3}$
\choice $\dfrac{1}{\sqrt{2}}$
\choice $\dfrac{1}{\sqrt{3}}$
\end{oneparchoices}
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\end{questions}
\end{document}